Measure of set A with random variables

Question

Let $\Omega=[0,1]$ and let $s$ be the Lebesgue measure restricted to $\Omega.$ Let $X(\omega)=\sin(2\pi\omega)$ and $Y(\omega)=\cos(2\pi\omega)$ be $2$ random variables on $\Omega$ where $\omega \in \Omega$. Let $A=\{\omega , X(\omega) > 1-a\} $ and $B=\{\omega , Y(\omega) > 1-a\}$ where $a>0$.

Then, what are $s(A)$,$s(B)$, s($A\cap B$)? Can you calculate them?